Question

If \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar vectors and \( \lambda \) is a real number, then the vectors \[ \vec{a} + 2\vec{b} + 3\vec{c}, \quad \lambda\vec{b} + 4\vec{c}, \quad (2\lambda - 1)\vec{c} \] are non-coplanar for:

• A. no value of \( \lambda \).
• B. all except one value of \( \lambda \).
• C. all except two values of \( \lambda \).
• D. all values of \( \lambda \).

Hint:

For non-coplanar vector problems: \begin{itemize} \item Use scalar triple product. \item Convert vectors into coefficient matrix. \item Nonzero determinant ⇒ non-coplanar. \end{itemize}

Answer 1

The Correct Option is B